Quantization Of Time And Energy

[steve_bank]

Putting aside QM for a bit.

Here time and energy are SI time and energy seconds and Joules. No metaphysics, physics.

All clocks are quantized mechanical, atomic, and electronic.

A mechanical clock can not have an infinite number of gears and teeth. Reducing gear size ends in quantum limits.

Atomic clocks derive the second by counting a finite number of particle radiation.
There is an averaging process so 1 second in the physical standard is not exactly 1.0 seconds.
An electronic clock uses discrete digital counters to create a second reference. It too ends in quantum limits. Your watch typically uses a 32kz crystal digitally divided.

Observed change is therefore quantized by time. The measurement of velocity is quantized.


The energy density of coal is about 24 mega Joules per kilogram. Coal is quantized by atoms. Burning coal can only create heat in integer multiples of 1 atom. Coal is not pure carbon, but primarily.

A rocket in deep space burns solid fuel. v = ds/dt a = dv/dt. f = ma. Force to change velocity, acceleration, can only change in integral multiples of of the atoms/molecules of fuel. I'd then argue that velocity can not change continuously.

 

[Juma]

There is not a one-to-one relationship between each atom in the reaction and the speed.
A lot of the energy becomes heat.

The space ship may hit small particles (or even large ones) and then its velocity depends on the momentum (speed, mass AND direction) and since monentum isnt quanticized then... you get the point, speed is neither.

You are overthinking thus quanta stuff. The only thing that is quanticized is electromagnetic radiation an that is because its a particle, the photon.

Energy is not generally quanticized.

 

[steve_bank]

I could find the thermal energy of 1 carbon atom, then calculate atoms per kg. It should add up to the approximations of 24MJ per kg. Energy is quantized. Fuel burns creating hot gas which creates thrust. The gas is quantized. If the fuel source is Joules per molecule then trust can only be integer multiples.

Consider a thought experiment. Initialy there is 1 gas molecule exiting the rocket engine. It reprents a finite discrte energy. What is the net increment? 2 molecules, then 3...


Thrust can only change in integer multiples of a gas. Heat creating the gas can only change in multiples of 1 molecule.

I burn 1 atom of coal per second creating heat. Then 2 per second... Heat can only change in discrete steps.

 

[Juma]

I could find the thermal energy of 1 carbon atom, then calculate atoms per kg. It should add up to the approximations of 24MJ per kg. Energy is quantized. Fuel burns creating hot gas which creates thrust. The gas is quantized. If the fuel source is Joules per molecule then trust can only be integer multiples.

Consider a thought experiment. Initialy there is 1 gas molecule exiting the rocket engine. It reprents a finite discrte energy. What is the net increment? 2 molecules, then 3...


Thrust can only change in integer multiples of a gas. Heat creating the gas can only change in multiples of 1 molecule.

I burn 1 atom of coal per second creating heat. Then 2 per second... Heat can only change in discrete steps.

That is an ridicilously oversimplified view of how a rocket works.
You have a lot of heat losses, not all of energy released by each burnt molecule contributes to speed.

 

[steve_bank]

I could find the thermal energy of 1 carbon atom, then calculate atoms per kg. It should add up to the approximations of 24MJ per kg. Energy is quantized. Fuel burns creating hot gas which creates thrust. The gas is quantized. If the fuel source is Joules per molecule then trust can only be integer multiples.

Consider a thought experiment. Initialy there is 1 gas molecule exiting the rocket engine. It reprents a finite discrte energy. What is the net increment? 2 molecules, then 3...


Thrust can only change in integer multiples of a gas. Heat creating the gas can only change in multiples of 1 molecule.

I burn 1 atom of coal per second creating heat. Then 2 per second... Heat can only change in discrete steps.

That is an ridicilously oversimplified view of how a rocket works.
You have a lot of heat losses, not all of energy released by each burnt molecule contributes to speed.

Efficiency is irrelevant, LOT does apply. Expanding gas works against the rocket and thrust results from Newton's 3rd Law, equal and opposite reaction.

Here and on another thread you seem to ignore QM and stick to Newtonian mechanics.

I have a bucket hanging on a rope. I drop a handful of ball bearings into bucket. The gravitational potential energy added to the bucket is quantized, integer multiples of on ball bearings. Do you really want to argue that?

I shoot a shotgun at an object. The momentum, or energy, transferred to the object is in multiples of finite kinetic energy and momentum of a single pellet. Agree or disagree?

A tank contains compressed argon with a pressure gauge attached. Is pressure continuous infinitely divisible or is it quantized? At higher pressures including atmospheric pressure, the gauge indicates the average energy of many atoms bouncing off the sensor. Rain falling on a car roof. Pressure is Newtons/m^2 or Pascals. Reduce the gas to a few hundred atoms and pressure has no meaning. Pressure is not continuous, it the the aggregate of many particles. Pressure can only change in increments of the energy of one atom of argon.

You continually seem to argue against the quantization inherent to QM.

 

[Juma]

I could find the thermal energy of 1 carbon atom, then calculate atoms per kg. It should add up to the approximations of 24MJ per kg. Energy is quantized. Fuel burns creating hot gas which creates thrust. The gas is quantized. If the fuel source is Joules per molecule then trust can only be integer multiples.

Consider a thought experiment. Initialy there is 1 gas molecule exiting the rocket engine. It reprents a finite discrte energy. What is the net increment? 2 molecules, then 3...


Thrust can only change in integer multiples of a gas. Heat creating the gas can only change in multiples of 1 molecule.

I burn 1 atom of coal per second creating heat. Then 2 per second... Heat can only change in discrete steps.

That is an ridicilously oversimplified view of how a rocket works.
You have a lot of heat losses, not all of energy released by each burnt molecule contributes to speed.

Efficiency is irrelevant, LOT does apply. Expanding gas works against the rocket and thrust results from Newton's 3rd Law, equal and opposite reaction.

Here and on another thread you seem to ignore QM and stick to Newtonian mechanics.

I have a bucket hanging on a rope. I drop a handful of ball bearings into bucket. The gravitational potential energy added to the bucket is quantized, integer multiples of on ball bearings. Do you really want to argue that?

I shoot a shotgun at an object. The momentum, or energy, transferred to the object is in multiples of finite kinetic energy and momentum of a single pellet. Agree or disagree?

A tank contains compressed argon with a pressure gauge attached. Is pressure continuous infinitely divisible or is it quantized? At higher pressures including atmospheric pressure, the gauge indicates the average energy of many atoms bouncing off the sensor. Rain falling on a car roof. Pressure is Newtons/m^2 or Pascals. Reduce the gas to a few hundred atoms and pressure has no meaning. Pressure is not continuous, it the the aggregate of many particles. Pressure can only change in increments of the energy of one atom of argon.

You continually seem to argue against the quantization inherent to QM.

I do not deny that QM correctly predicts that some aspects are quantized.
That doesnt mean that everything is quantized.
That something are quantized means that it can be written as x=k*n where k is a universal constant.
That there are only certain values that are allowed.
As you know a lot of the energy that comed from molecular movement becomes thermal energy, heat. Some of that heat will dissipate into other parts if the ship and how much will vary greatly between different molecules. And that variation is not quantized. thus you cannot assume that all chemical energy will result in velocity.

A free electron can have any energy. Its not quantized.

An electron trapped on a potential well on the other side, can only have specific energy levels specified by the nature of the well.

Etc.

Velocity, mass, energy etc isnt quantized per se.

And yes, this is exactly what QM states.

 

[steve_bank]

You can accelerate an electron, but how do you transfer energy to it?

In a particle accelerator at the bottom is a power supply that supplies energy to the accelerating magnets. The output of the supply be it current or voltage can only change in ratios of electrons. If I trace the mains back to the generator it is quantized. Natural gas, coal, and uranium reduce to atoms and particles in sufficient quantities to appear continuous..

Whenever you drill down into what appears to be continuous Newtonian variables you will find quantization. Beneath our stable macro reality per QM is a reality of particles and probabilities.

 

[Jokodo]

You can accelerate an electron, but how do you transfer energy to it?

In a particle accelerator at the bottom is a power supply that supplies energy to the accelerating magnets. The output of the supply be it current or voltage can only change in ratios of electrons. If I trace the mains back to the generator it is quantized. Natural gas, coal, and uranium reduce to atoms and particles in sufficient quantities to appear continuous..

Whenever you drill down into what appears to be continuous Newtonian variables you will find quantization. Beneath our stable macro reality per QM is a reality of particles and probabilities.

I could find the thermal energy of 1 carbon atom, then calculate atoms per kg. It should add up to the approximations of 24MJ per kg. Energy is quantized. Fuel burns creating hot gas which creates thrust. The gas is quantized. If the fuel source is Joules per molecule then trust can only be integer multiples.

Consider a thought experiment. Initialy there is 1 gas molecule exiting the rocket engine. It reprents a finite discrte energy. What is the net increment? 2 molecules, then 3...


Thrust can only change in integer multiples of a gas. Heat creating the gas can only change in multiples of 1 molecule.

I burn 1 atom of coal per second creating heat. Then 2 per second... Heat can only change in discrete steps.

That is an ridicilously oversimplified view of how a rocket works.
You have a lot of heat losses, not all of energy released by each burnt molecule contributes to speed.

Efficiency is irrelevant, LOT does apply. Expanding gas works against the rocket and thrust results from Newton's 3rd Law, equal and opposite reaction.

Here and on another thread you seem to ignore QM and stick to Newtonian mechanics.

I have a bucket hanging on a rope. I drop a handful of ball bearings into bucket. The gravitational potential energy added to the bucket is quantized, integer multiples of on ball bearings. Do you really want to argue that?

I shoot a shotgun at an object. The momentum, or energy, transferred to the object is in multiples of finite kinetic energy and momentum of a single pellet. Agree or disagree?

The kinetic energy of a single pellet is finite, but not constant. Even if the energy at the muzzle were constant (quite an assumption by itself), the energy transferred to the object not only depends on the pellet's own momentum, but also on its angle. And even the pellet' momentum at the time of impact isn't going to be constant: It depends on how much it has lost in a series of impact with air molecules, coming in at all sorts of angles with all sorts of velocities. In order to treat this as evidence that the momentum imparted on your target is quantized, you're assuming that the momentum of air molecules has to be quantized (as well as angles).

That's some serious circular reasoning!

A tank contains compressed argon with a pressure gauge attached. Is pressure continuous infinitely divisible or is it quantized? At higher pressures including atmospheric pressure, the gauge indicates the average energy of many atoms bouncing off the sensor. Rain falling on a car roof. Pressure is Newtons/m^2 or Pascals. Reduce the gas to a few hundred atoms and pressure has no meaning. Pressure is not continuous, it the the aggregate of many particles. Pressure can only change in increments of the energy of one atom of argon.

Pressure isn't measured in atoms. The closest you could get is saying that pressure is measured as the sum of the momentum of atoms hitting the encasing per unit of time. For pressure to be quantized, it's not enough that atoms are quantized: time and momentum too have to be!

 

[steve_bank]

Pressure in a tank is macroscopic effect of a lot of atoms bouncing off a sensor surface. It is not a continuum. Atoms are in motion. Newtonian pressure can only change in discrete steps of atoms. If pressure is not the sum of of discrete atoms kinetic energy, then what is it? Atoms have mass. At room temperature as the gas reaches equilibrium they sete towards the bottom of the tank creating a layered density. The ambient thermal energy keeps the atoms in motion.

No different than Newtonian mechanics overall. We use it to send a probe to the Moon, but NM is the result of a large aggregate of particles.

When the cluster of pellets hit an object the total energy/momentum transfer is the sum of the finte energies of the pellets at the time of impact. What happens at the muzzle is irrelevant.

 

[Jokodo]

Pressure in a tank is macroscopic effect of a lot of atoms bouncing off a sensor surface.

That's what I said: It's the macroscopic effect of the number of atoms bouncing of per second times their average momentum. An atoms momentum in turn is determined by its mass and velocity.

Only one of those factors, mass, is a discrete and fixed quantity per atom.

It is not a continuum. Atoms are in motion. Newtonian pressure can only change in discrete steps of atoms.

Assuming constant and/or quantized hit rates and average momentum. Not a given unless you first show that velocity/momentum is quantized. Either that, or pretending that mass is the only contributing factor, which is false per the above.

If pressure is not the sum of of discrete atoms kinetic energy, then what is it?

It is. Is kinetic energy determined by the discrete quantity of atoms' mass alone? I would have thought atoms' motion vectors also play a role.

Atoms have mass. At room temperature as the gas reaches equilibrium they sete towards the bottom of the tank creating a layered density. The ambient thermal energy keeps the atoms in motion.

No different than Newtonian mechanics overall. We use it to send a probe to the Moon, but NM is the result of a large aggregate of particles.

When the cluster of pellets hit an object the total energy/momentum transfer is the sum of the finte energies of the pellets at the time of impact. What happens at the muzzle is irrelevant.

The "sum of the finite energies of the pellets at the time of impact" is correct. But you're assuming that those are identical. That is unlikely to be the case in any real world scenario (that is, unless you do the experiment in a perfect vacuum). The pellets all loose velocity and with it kinetic energy as they travel through air, some more than others (because they're caught in a wind gust, or simply because the sum of the random directions of the gas molecules they interact with doesn't quite equal 0).

 

[steve_bank]

That's what I said: It's the macroscopic effect of the number of atoms bouncing of per second times their average momentum. An atoms momentum in turn is determined by its mass and velocity.

Only one of those factors, mass, is a discrete and fixed quantity per atom.



Assuming constant and/or quantized hit rates and average momentum. Not a given unless you first show that velocity/momentum is quantized. Either that, or pretending that mass is the only contributing factor, which is false per the above.

If pressure is not the sum of of discrete atoms kinetic energy, then what is it?

It is. Is kinetic energy determined by the discrete quantity of atoms' mass alone? I would have thought atoms' motion vectors also play a role.

Atoms have mass. At room temperature as the gas reaches equilibrium they sete towards the bottom of the tank creating a layered density. The ambient thermal energy keeps the atoms in motion.

No different than Newtonian mechanics overall. We use it to send a probe to the Moon, but NM is the result of a large aggregate of particles.

When the cluster of pellets hit an object the total energy/momentum transfer is the sum of the finte energies of the pellets at the time of impact. What happens at the muzzle is irrelevant.

The "sum of the finite energies of the pellets at the time of impact" is correct. But you're assuming that those are identical. That is unlikely to be the case in any real world scenario (that is, unless you do the experiment in a perfect vacuum). The pellets all loose velocity and with it kinetic energy as they travel through air, some more than others (because they're caught in a wind gust, or simply because the sum of the random directions of the gas molecules they interact with doesn't quite equal 0).

Atomic motion vectors? A gas particle at high density should have an instantaneous vector, but gas atoms are bouncing off of each other in the tank. The path of an atom is determined by probabilities. It is not Newtonian. The actual equations for modeling gas atoms in a tank I'd have to look up. Energy is exchanged between atoms in collisions with each other and the tank wall.

I spent a year in a pressure sensor group. Strain gauges were deposited on a saphire disk. Harsh environments like jet engine oil pressure. They also made fuel true mass rate flow sensors for jets. I worked with hydraulics.

That is not what you said, but no matter. We then agree that pressure in a tank is quantized? It is the instantaneos sum of all the atoms on an area of a tank?

Now you are expressing the difference between Newtonian and quantum. The Newtonian moon is the moment by moment result of a large number of particles the individual states described by probabilities.

The shotgun was an analogy. Throw a homogeneous piece of aluminum. Discrete atoms with discrete mass are held in place by interatomic forces. Kinetic energy of the block can only be the sum of the discrete energy of each atom. The kinetic energy of the block is quantized. The only way to dispute that is to argue against atomic and quantum physics. If I stick a bunch of BBs together and throw it , a macroscopic analogy. With enough BBs stuck together I can treat the mass as a continuum, like a billiard ball.

Time is quantized as I described. Time being SI time as a measure of change, as in determining velocity.

No matter which way you go you end up with quantization. Newtonian is the result of a the stages of a large number of discrete states.

 

[Kharakov]

Putting aside QM for a bit.
...
A rocket in deep space burns solid fuel. v = ds/dt a = dv/dt. f = ma. Force to change velocity, acceleration, can only change in integral multiples of of the atoms/molecules of fuel. I'd then argue that velocity can not change continuously.

Uhuh. It does though. There are no completely non-elastic collisions or emissions (collisions/emission should cover your rocket's physics) in reality.

And it (velocity) changes continuously if GR describes real phenomena. So.... you have that too.

 

[Jokodo]

That's what I said: It's the macroscopic effect of the number of atoms bouncing of per second times their average momentum. An atoms momentum in turn is determined by its mass and velocity.

Only one of those factors, mass, is a discrete and fixed quantity per atom.



Assuming constant and/or quantized hit rates and average momentum. Not a given unless you first show that velocity/momentum is quantized. Either that, or pretending that mass is the only contributing factor, which is false per the above.



It is. Is kinetic energy determined by the discrete quantity of atoms' mass alone? I would have thought atoms' motion vectors also play a role.



The "sum of the finite energies of the pellets at the time of impact" is correct. But you're assuming that those are identical. That is unlikely to be the case in any real world scenario (that is, unless you do the experiment in a perfect vacuum). The pellets all loose velocity and with it kinetic energy as they travel through air, some more than others (because they're caught in a wind gust, or simply because the sum of the random directions of the gas molecules they interact with doesn't quite equal 0).

Atomic motion vectors? A gas particle at high density should have an instantaneous vector, but gas atoms are bouncing off of each other in the tank.

So? How does that imply it's discrete?

The path of an atom is determined by probabilities.

So? How does that imply discreteness?

It is not Newtonian.

I believe gas molecules' motions can be largely, if not entirely, explained in a Newtonian framework. But assume I'm wrong: How does that imply discreteness?

The actual equations for modeling gas atoms in a tank I'd have to look up. Energy is exchanged between atoms in collisions with each other and the tank wall.

... and unless energy is discrete and quantized and so is time, this will lead to pressure as a continuous measure.

I spent a year in a pressure sensor group. Strain gauges were deposited on a saphire disk. Harsh environments like jet engine oil pressure. They also made fuel true mass rate flow sensors for jets. I worked with hydraulics.

Then ask your then colleagues if pressure can be equated with number of atoms. Or better don't, they'll wonder what happened to their once smart colleague.

That is not what you said, but no matter. We then agree that pressure in a tank is quantized?

We definitely don't. You made no argument that it is.

It is the instantaneos sum of all the atoms on an area of a tank?

It's not the "sum of all the atoms". It's the sum of the atoms' momentum as they hit the tank wall per unit of time, per unit of wall surface area. Momentum, in turn, is mass * velocity. While the atoms mass is quantized (at least approximately and under Newtonian assumptions: with relativity, mass depends on velocity), velocity, time, and area/space aren't. At least you have provided no non-circular argument to believe they are.

 

[steve_bank]

Putting aside QM for a bit.
...
A rocket in deep space burns solid fuel. v = ds/dt a = dv/dt. f = ma. Force to change velocity, acceleration, can only change in integral multiples of of the atoms/molecules of fuel. I'd then argue that velocity can not change continuously.

Uhuh. It does though. There are no completely non-elastic collisions or emissions (collisions/emission should cover your rocket's physics) in reality.

And it (velocity) changes continuously if GR describes real phenomena. So.... you have that too.

Have gravitons been demonstrated? Gravity is quantized is it not?

 

[steve_bank]

Well jokoo do, if you agree that pressure is the average of the finite energies of particles striking a surface and reject pressure as quantized is contradictory. As all Newtonian variables at a high enough density in the tank we treat pressure as infinitely divisible.

I can not do it off the top of my head I'd have to work on an equation. It requires statistical mechanics. Roughly the atoms in the tank are in continuous collisions with each other and the tank. Collisions with the tank transfer thermal energy to the gas. There is a probability of an atom hitting the tank at any point on the surface. The result will be a probability distribution defining how many atom strike an area of the tank at any instant.All particles may not have the same energy.

Rain falling on your car roof if heavy enough although quantized as drops will sound continuous. The total kinetic energy transferred to the roof is the sum of the drops each having finite energy. You appear to lack imagination, unable to visualize.

Your arguments are specious at best. I don't run off and email others for support.

You can't have it both ways. If you accept atoms as having discrete mass and energy you can't reject that the force on the surface of a tank can only change in discrete multiples. Fill a tank with marbles, does the force on the walls and bottom vary continuously or in steps of the mass of the marbles and gravitational energy?

 

[Jokodo]

Well jokoo do, if you agree that pressure is the average of the finite energies of particles striking a surface and reject pressure as quantized is contradictory.

Not the average, the sum. More importantly, though, the sum of their energies striking a surface per unit of time, per unit of surface area. In order for pressure to be quantized, it's not enough for their energies to be quantized, time and space would have to be too. Even if we accept your claim that energy is quantized (not something you've demonstrated either), the conclusion that pressure is quantized is like saying "if you accept that the Netherlands are in Europe, your rejection of the conclusion that Europe's area is 41,543 km² (the area of the Netherlands) is contradictory".

As all Newtonian variables at a high enough density in the tank we treat pressure as infinitely divisible.

I can not do it off the top of my head I'd have to work on an equation. It requires statistical mechanics. Roughly the atoms in the tank are in continuous collisions with each other and the tank. Collisions with the tank transfer thermal energy to the gas. There is a probability of an atom hitting the tank at any point on the surface. The result will be a probability distribution defining how many atom strike an area of the tank at any instant.All particles may not have the same energy.

Rain falling on your car roof if heavy enough although quantized as drops will sound continuous. The total kinetic energy transferred to the roof is the sum of the drops each having finite energy.

Yes, and? Drops come at all kind of velocities, so in order to show that the kinetic energy is quantized, you still need to demonstrate that velocity is quantized. Depending on the local air density, they are slowed more or less by drag. Larger drops are generally less affected by air drag than smaller drops, and while drop sizes are multiples of one molecule of water, the relationship is non-linear. Furthermore, they don't fall as perfect spheres but are continually distorted by the same air drag during their fall, changing their shapes, and with it the amount of resistance and thus their velocity continually changes even given a certain air density, so even in one and the same spots, they'll be coming in at different velocities.

Only in a perfect vacuum, and then only if they've been released at the exact same vertical distance from whichever spot on your car they're going to hit* would the drops be all coming in at a fixed velocity, and thus their energy be determined by a linear relation to their mass, quantized as multiples of the mass of a water molecule.

How often do you park in a perfect vacuum?

You appear to lack imagination, unable to visualize.

Your arguments are specious at best. I don't run off and email others for support.

You can't have it both ways. If you accept atoms as having discrete mass and energy you can't reject that the force on the surface of a tank can only change in discrete multiples. Fill a tank with marbles, does the force on the walls and bottom vary continuously or in steps of the mass of the marbles and gravitational energy?

Gas pressure doesn't work like that, it's caused almost entirely by the molecules impacting the walls (bottom and lid included), with the weight of the molecules under standard Earth gravity being an all but negligible contributor to pressure at the bottom. It's true that the molecules' paths are, in theory, parabolic, and thus there'll be slightly more molecules near the bottom than near the top at any one time and the bottom will get slightly more hits than the top, but outside of an ultra-high-vacuum chamber at temperatures near absolute zero, a molecule will typically (that is to say, almost invariably) be colliding with another or the casing long before this deviation from a linear path becomes apparent.

But assume a closed tank with the marbled packed so tightly that they're pressing not only against the bottom and the sides, but also against the top: The pressure will indeed vary continuously e. g. if you add heat to the setup: depending on whether whatever material the tank is made from expands more or less under heat than glass, pressure will decrease or increase with temperature; or if you move in the walls, reducing the size of the tanks along continuous space, pressure will increase continuously.



* To be precise, not even then: consider a droplet that has been released 100 meters above your hood, thus say 101.0 meters above ground, and one that's been released 100 meters above your roof, or 101.5 meters above ground. Considering that gravity diminishes with distance, one of them will have been accelerated more than the other throughout its journey, and thus have a higher velocity at impact even in a perfect vacuum. So in order for your conclusion that the impact energy is quantized because water drops are quantized to follow, not only do we need to assume a perfect vacuum, but also we'd have to pretend that gravitational acceleration is altitude-invariant.

 

[Jokodo]

And anyway, in a perfect vacuum, the water drops would instantly vaporize. Your scenario requires air to work at all but requires a perfect vacuum (plus a few more unrealistic assumptions) to show what you want it to show. Who's contradicting themselves now?

 

[steve_bank]

And anyway, in a perfect vacuum, the water drops would instantly vaporize. Your scenario requires air to work at all but requires a perfect vacuum (plus a few more unrealistic assumptions) to show what you want it to show. Who's contradicting themselves now?

I think and reason in images supported by math. When I think about a tank of gas I see a 3D picture of the molecules colliding with each other and the tank. The best people I worked with had the ability to communicate by analogy and metaphor. Wrote theory alone is insufficient. The ability can be developed.

If you do not see the analogy of rain to a gas in a tank hitting the wall then you are inexperienced, narrow minded, or just being stubborn.




One last time. If you accept quantization of matter as atoms which have finite mass and finite thermal energy for fuels thne the total energy of a bucket of gas is the sum of the finite energy of each molecule. Reject that then nothing more to say.

From his bio AE attributed an uncle for his ability to visualize. He would imagine himself traveling along light at C. You do not seem to understand what analogy and thought experiment is.

http://www.vicphysics.org/documents/teachers/unit3/EinsteinsTrainGedanken.pdf

Gedanken experiment. A common tool.

https://physics.stackexchange.com/q...that-lead-to-the-special-theory-of-relativity

After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with a velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing. . . on the basis of experience. . . . From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how, otherwise, should the first observer know, that is, be able to determine, that he is in a state of fast uniform motion?

https://en.wikipedia.org/wiki/Thought_experiment



Schrödinger's cat (1935) presents a cat that is indeterminately alive or dead, depending on a random quantum event. It illustrates the counterintuitive implications of Bohr's Copenhagen interpretation when applied to everyday objects.
A thought experiment (German: Gedankenexperiment,[1] Gedanken-Experiment[2] or Gedankenerfahrung[3]) considers some hypothesis, theory,[4] or principle for the purpose of thinking through its consequences. Given the structure of the experiment, it may not be possible to perform it, and even if it could be performed, there need not be an intention to perform it.

The common goal of a thought experiment is to explore the potential consequences of the principle in question:

 

[steve_bank]

Back to basics.

The derivative of the velocity with respect to energy of a particle is

dv = [(2/m)^1/2] * [1(2*x^1/2)] dE where v is velocity and E energy.


For a finite change in energy dE there is a finite change in velocity dv. If you claim dE is infinitely divisible then site an energy source that is not quantized, compared to coal and gasoline.

 

[steve_bank]

wrong thread